Answer
$0.58$, $2.56$, $3.72$, $5.70$
Work Step by Step
$5\cos 2\theta=2$
$\cos 2\theta=\frac{2}{5}$
$2\theta=\dots$, $-1.16$, $1.16$, $5.12$, $7.44$, $11.41$, $13.73$, $\dots$
$\theta=\dots$, $-0.58$, $0.58$, $2.56$, $3.72$, $5.70$, $6.86$, $\dots$
Since we only want solutions in $[0, 2\pi)$, our answers are $0.58$, $2.56$, $3.72$, and $5.70$.
